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This paper deals with numerical approximation of the following quasilinear parabolic equation ut = uuxx, 0 < x < 1, t > 0, with a nonlinear boundary condition ux(0, t) = −u(0, t), ux(1, t) = 0, t > 0. We show that the solution of the semidiscrete scheme, obtained by the finite differences method blows up in a finite time when 0 < q < 1. Convergence of the numerical blow-up time to the theoretical one when the mesh size goes to zero is also established. Finally, we give some numerical results to illustrate certain point of our work.

NUMERICAL BLOW-UP ON WHOLE DOMAIN FOR A QUASILINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION